Some verbs are not conceptualized, natively, as being possible to do in a "continuous" way. One can't be in the process of sitting. One is either sat or not-sat. I agree that a variety of English translations can be accepted, however the Hindi sentence you wrote is not idiomatic.
Curious: how would one express, "while he was sitting down, someone pulled his chair out from under him." That being said, this explanation seems to he the most accurate. Basically, English (unlike most languages) now mainly reserves the present tense for habitual actions ("every week"). The result is a 1:2 relationship between a present tense (non-continuous) hindi verb construction (even if it is adjectival) and the english structures of continuous or habitual action. In most cases, therefore, both translations should be acceptable ("sits" or "is sitting"). Sorry, but 1:1 "consistency" is simply impossible. All languages are adequate for describing all thoughts and ideas, but they simply chop them up differently based on what the current grammar and vocabulary allow for (usually based on a balance of competing priorities: simplicity and accuracy).
The vowel in बैठा can be said like the A in English "bat" The vowel in बेटा can be said like the AI in English "bait." Maybe not exactly, yada yada, but close enough to make the relevant distinction.
The best way to make the distinction though, is to really lean into the added air (aspiration) in बैठा, and make sure you're not putting any air on बेटा. Although I don't hear anything wrong with the Duo recording, I do find hearing the aspiration to be a bit harder to hear than, perhaps, it is with a live speaker.
The e in "bet" and the a in "bat" are allophones in Hindi. Either works; both have the same communicative value, phonemically.
From a precise phonetic perspective, our tow English "bat"'s may differ somewhat, too. So of course, saying the sound is like "so and so" in English is imprecise but, like I said, close enough.
Whether the Hindi vowel sounds more like "bet" or "bat" actually varies across Hindi. The important thing is that this variation is not meaningful, and that either/both are meaningfully distinguished from the vowel in बेटा :) https://youtu.be/_EaX17bVcwc